intersection of sets

交

Foundations & Logic · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

The intersection of A and B contains exactly the objects belonging to both.

A 与 B 的交恰由同时属于二者的对象组成。

Example

{2,5}∩{5,7}={5}\{2,5\}\cap\{5,7\}=\{5\}.

Usage and distinctions

An empty indexed intersection needs an ambient universe; it is not an unrestricted universal set in ZF.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§11.1 Elementary Set Theory; §11.4 Cartesian Product and Power Set · Checked 2026-10-14

Translation sources

  1. 李文威 — 代数学方法，第一卷（作者源码）第1章：「ZFC 公理一览」，派生运算段「交 X∩Y」 · Checked 2026-10-14
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